Two-echelon Location-routing Problem Research Articles

Sustainable urban logistics: A case study of waterway integration in Amsterdam

This paper tackles the growing challenges in urban logistics by presenting an optimal distribution network that integrates urban waterways and last-mile delivery, tailored for cities boasting extensive waterway networks. We examine Amsterdam's city center as a case study, prompted by the strain on quay walls, congestion, and emissions, urging a reevaluation of its urban logistics design. We formulate the problem as a two-echelon location routing problem with time windows and introduce a hybrid solution approach for effective resolution. Our algorithm consistently outperforms existing methods, with a superior solution quality, demonstrating its effectiveness across established and newly developed benchmark instances. In our case study, we evaluate the benefits of transitioning from a roadway-centric to a waterway-based system, showcasing significant cost savings (approximately 28 %), reductions in vehicle weight (approximately 43 %), and minimized travel distances (approximately 80 %) within the city center. The integration of electric vehicles enhances environmental sustainability, resulting in a total daily emission reduction of 43.46 kg. Our study underscores the untapped potential of inland waterways in easing urban logistics challenges. Inspired by Amsterdam's experience, global cities can adopt innovative approaches for sustainable logistics, providing valuable insights for managers striving to enhance efficiency, cut costs, and promote sustainable transportation practices.

Two-Echelon Location–Routing Problem of Perishable Products Based on the Integrated Mode of In-Store Pick-Up And Delivery

The integrated service mode of in-store pick-up and delivery has become common in the post-epidemic period owing to the combined online and offline purchases of perishable products. This study investigates the diverse requirements of in-store pick-up and delivery customers. Then, it establishes a two-echelon location–routing model for a perishable food distribution network to minimize total cost as an objective. An adaptive large neighborhood search (ALNS) algorithm was also developed to solve the foregoing problem. To test the algorithm, instances from those of Solomon are derived. The proposed ALNS algorithm was found to achieve satisfactory performance with respect to speed and accuracy by comparing its results with those of the CPLEX software for a 12-node small-scale instance. The applicability and stability of the ALNS algorithm were further verified using different types of instances with more nodes. Different proportions of in-store pick-up and delivery customers were set, and the total cost of location–routing schemes under these proportions was compared. The results show that an integrated service type compared with the single delivery service mode and single in-store pick-up service mode can save 7.98% and 11.44% of the total cost, respectively.

An exact algorithm for Two-Echelon Location-Routing problem with simultaneous pickup and delivery

This study considers an extension of the two-Echelon Location-Routing Problem (2E-LRP) namely two-Echelon Location-Routing Problem with Simultaneous Pickup and Delivery (2E-LRPSPD). A Mixed Integer Programming (MIP) formulation is developed and strengthened by the use of valid inequalities to solve the 2E-LRPSPD, and then a Branch and Cut-based exact algorithm (B&C) is presented. To improve the upper bounds, Iterated Local Search and Variable Neighborhood Search-based metaheuristic algorithms, namely, ILS-VNS and VNS, are developed and embedded into the B&C. Computational results, conducted on instances produced from the literature, demonstrate that the B&C yields tight lower and upper bounds, and also is capable of solving some instances optimally with up to 50 customers and 10 satellites in a reasonable time. Furthermore, sensitivity analysis reveals that the heuristic approaches and an increase in the runtime limit assist the algorithm to reach tight the upper bounds, whereas the number of potential depots does not have any effect on the performance of the algorithm. Besides, further computational analysis on the 2E-LRPSPD with a single depot, which is studied in the literature, shows that the B&C improves some best-known solutions while proving the optimality of some instances. Finally, the B&C is applied to a two-echelon supermarket distribution system in Türkiye. The computational results show that simultaneous pickup and delivery operations, as well as depot location decisions are critical elements to consider in the design of cost-effective distribution networks.

A branch-and-price method for a two-echelon location routing problem with recommended satellites

In city logistics, the two-echelon location routing problem is crucial in coordinating resources and radiating nodes, enabling the efficient planning of relay stations and vehicle distribution routes. However, with the expansion of distribution scopes and changes in urban development, fixed relay stations may not be able to adapt to the evolving network demand structure, leading to reduced efficiency. This paper proposes a two-echelon location routing problem with recommended satellites (2E-LRPRS) to address this issue. These satellites are chosen from the customer set and can be reoptimized to enhance the network's adaptability. A mixed-integer linear program (MILP) is formulated to minimize the distribution cost of the two-echelon network. To solve this problem, a column-generation algorithm (CG) is proposed, which decomposes the original problem into a linear relaxation main problem and a series of two-stage shortest-path subproblems with resource constraints. The branch-and-pricing algorithm (B&P) is then designed to obtain the integer solution. The experimental results demonstrate that the proposed B&P is significantly more efficient and effective than the MILP solver - Cplex. Furthermore, by selecting relay stations from customers, the recommended satellites can be flexibly adjusted based on the locations and demands of distribution customers, leading to an average operating cost savings of 8.43%.

A mathematical optimization model for cluster-based single-depot location-routing e-commerce logistics problems

This study proposes a mathematical optimization model for a two-echelon location-routing problem in the last-mile delivery e-commerce environment. The e-commerce firm delivers each customer’s demand at home or through delivery points. Customers could be unavailable when the vehicle arrives at their homes. In this case, the vehicle must visit the allocated delivery points for the unavailable customer. There are several scenarios from all-present to all-absent customers. A mathematical model is proposed with six inequalities to reduce the model’s complexity. In addition, two scenario reduction methods are introduced to deal with the exponential growth of the number of scenarios. We generate twelve numerical instances to evaluate the performance of the model, the scenario reduction methods, and the proposed inequalities. The model produces valid solutions. Also, the scenario reduction methods are helpful for decision-makers in the e-commerce context by reducing the number of scenarios and decreasing the complexity of managing unavailable customer scenarios.

A two-echelon location routing problem considering sustainability and hybrid open and closed routes under uncertainty

Location-routing is an extremely important problem in supply chain management. In the location-routing problem, decisions are made about the location of facilities such as distribution centers as well as the set of vehicle routes. Today, organizations seek to reduce the transportation cost by outsourcing leading to a particular kind of transportation problems known as open routing. However, the increasing attention to environment have led to paying more attention to environmental issues and reducing the environmental impacts of logistics activities. To this end, in this paper, both open and closed routes were simultaneously addressed by developing a multi-objective mixed integer linear programming model that included three economic, environmental, and social responsibility aspects. The three objective functions of the proposed model encompass the minimization of total costs and greenhouse gas emissions, and the maximization of employment rate and economic development. Also, in this study, a different type of routing was considered in each echelon. A small-sized problem instance was solved using the Augmented Epsilon Constraint (AEC) method with the CPLEX Optimizer Solver for the validation of the proposed model. Moreover, the sensitivity analysis was performed to investigate the effect of changing main parameters on the values of the objective function. Due to the NP-Hardness of the problem, two efficient metaheuristic algorithms of Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Stochastic Fractal Search (MOSFS) were exploited to solve the medium and large size problems. The performance of the algorithms was compared on the basis of six different well-known indexes of Time, MID, RAS, Diversity, Spacing, and SNS. According to the obtained results, the performance of the MOSFS algorithm was %20, %9, %11.22, %10.03, and %19.06 higher than the performance of the NSGA-II on the basis of SNS, RAS, MID, Diversity, and Time indexes, respectively. On the other hand, the NSGA-II performance was %6.3 higher than the MOSFS performance in terms of Spacing index.

A two-echelon location routing problem with mobile satellites for last-mile delivery: mathematical formulation and clustering-based heuristic method.

In last-mile delivery, the turbulence of traffic uncertainties is often solved by establishing and utilizing multiple buffering warehouses (satellites) with setup and operational costs, which are very costly in implementation. This distribution system involving satellites is often derived as the two-echelon location routing problem (2E-LRP). This study proposes a new variety of 2E-LRP problems with mobile satellites, called 2E-LRP-MS, which aims to reduce the cost of 2E-LRP by replacing fixed-located satellites with mobile satellites. Rather than utilizing fixed-location satellites, 2E-LRP-MS employs the first echelon vehicles (CT) as the mobile satellites moving around the city to replenish multiple second echelon vehicles (CF) en-route. For the cargo replenishment process, CT and CF can temporarily park at the consolidation points (CP), such as public parking lots or paid loading-unloading zones. With this flexibility, the high operational costs of the fixed-location satellites can be exchanged with CP's relatively low maintenance or renting fees, such as parking expenses. In this work, we introduce a heuristic method called clustering-based simultaneous neighborhood search (CSNS) to solve the proposed 2E-LRP-MS problem. The proposed CSNS considers the probabilistic mechanism and k-means clustering algorithm for facility selection, simultaneous neighborhood search to generate the routing solution, and local searches for optimizing the routing solution. Experimental results highlight the flexibility advantage of 2E-LRP-MS over 2E-LRP models and the searching efficiency of the proposed CSNS over the recent heuristic methods for two-echelon routing problems and commercial solver CPLEX.

Integrated Mathematical Model for Two-Echelon Location-Routing Problem and Application in a Public Institution

Lokasyon-rotalama problemi (LRP), stratejik ve taktik düzeydeki lojistik planlama kararlarına ilişkin en önemli optimizasyon problemlerinin başında gelmektedir. Bu çalışmada, ülkemizdeki bir kamu kurumunda karşılaşılan gerçek bir taşıma ağının özelliklerinden yola çıkılarak iki kademeli özgün bir LRP tanımlanmıştır. Çalışmanın amacı, iki kademeli LRP’de lokasyon ve rotalama kararlarını eş zamanlı olarak ele alan bütünleşik bir çözüm yaklaşımı aracılığıyla taşıma maliyetlerini en aza indirmeye yönelik bir taşıma ağının tasarlanmasıdır. Bu amaç doğrultusunda, iki kademeli LRP’nin bütünleşik bir şekilde çözümü için tamsayılı bir doğrusal programlama modeli geliştirilmiştir. Çalışmada incelenen problemin özelliklerine uygun olarak değişken kapalı uçlu araç rotalama tanımı yapılmıştır. Önerilen modelde, taşıma ağında yer alacak aktarma merkezi (AKM) sayısı ve lokasyonlarının belirlenmesine, talep merkezlerinin bu AKM’lere atanmasına ve her bir AKM için değişken kapalı uçlu araç rotalarının oluşturulmasına çalışılmıştır. Modelde birinci öncelikli amaç olarak taşıma ağı boyunca katedilen toplam mesafenin, ikinci öncelikli amaç olarak ise kullanılan toplam araç sayısının minimize edilmesi hedeflenmiştir. Geliştirilen model, kamu kurumunda karşılaşılan taşıma problemine uygulanmış ve modelin çözümü sonucunda oluşturulan taşıma ağı mevcut ağ ile karşılaştırılmıştır. Elde edilen çözüm sonuçları, önerilen taşıma ağı yoluyla sistem performansında önemli düzeyde iyileştirmelerin sağlanabileceğini göstermiştir.

A Branch-and-Price Method for a Two-Echelon Location Routing Problem with Recommended Satellites

A Branch-and-Price Method for a Two-Echelon Location Routing Problem with Recommended Satellites

The impact of loading restrictions on the two-echelon location routing problem

The two-echelon location routing problem (2E-LRP) arises in freight distribution when goods available at different origins are delivered to their respective destinations via intermediate facilities. The literature concerning the 2E-LRP considers freight capacities of vehicles to be scalars, while customer demands are additive volumes of individual items. However, ignoring the real dimensions of items and vehicles can lead to infeasible load plans in practice. Further investigation is thus required to study the impact of realistic loading restrictions on the 2E-LRP, algorithms for the problem and the quality of the solutions produced by those algorithms. This paper introduces a generalized 2E-LRP with two-dimensional loading restrictions (2E-LRP2L). To investigate how exactly one should handle these restrictions we introduce a heuristic optimization method combined with different loading strategies and evaluate their performance on instances derived from real-world data. Given that we are introducing a new problem, the quality of our heuristic is assessed by comparing it against state-of-the-art 2E-LRP methods on benchmark instances. The results indicate that the proposed method is highly competitive, finding most best-known solutions as well as providing some new ones.

A multi-objective two-echelon location-routing problem for cash logistics: A metaheuristic approach

This study proposes a two-echelon location routing framework for cash-in-transit. In order to mitigate the risk of robbery in cash transportation, a dynamic risk index is considered. The utilized risk function encompasses both the amount of cash carried by a vehicle and the travel time of a route, and it relaxes a pre-defined parameter of risk threshold in the literature. Multiple exact and metaheuristic methodologies are utilized and evaluated on several small to medium-sized instances and a case study. The effectiveness of the proposed methods is evaluated and shown by examining various multi-objective performance measures. The case study is researched in more depth to obtain managerial insights, and the results show that depending on the risk or cost efficiency of the solutions on a Pareto frontier, the risk of traversing longer routes or transporting larger amounts of cash can be determining in locating new bank vaults.

Two-Echelon Location-Routing Problem with Time Windows and Transportation Resource Sharing

In this work, a two-echelon location-routing problem with time windows and transportation resource sharing (2E-LRPTWTRS) is solved by selecting facility locations and optimizing two-echelon vehicle routes. The optimal solutions improve the efficiency of a logistics network based on the geographical distribution and service time windows of logistics facilities and customers. Furthermore, resource utilization is maximized by enabling resource sharing strategies within and among different logistics facilities simultaneously. The 2E-LRPTWTRS is formulated as a biobjective optimization model, and obtaining the smallest number of required delivery vehicles and the minimum total operating cost are the two objective functions. A two-stage hybrid algorithm composed of k-means clustering and extended multiobjective particle swarm optimization algorithm is proposed for 2E-LRPTWTRS optimization. A self-adaptive mechanism of flight parameters is introduced and adopted during the iterative process to balance the evolution of particles and improve the efficiency of the two-stage hybrid algorithm. Moreover, 20 small-scale instances are used for an algorithm comparison with multiobjective genetic algorithm and nondominated sorting genetic algorithm-II, and the solutions demonstrate the superiority of the proposed algorithm in optimizing logistics networks. The proposed optimization model and hybrid algorithm are tested by employing a real-world case of 2E-LRPTWTRS in Chongqing, China, and the optimization results verify the positive role of the developed model and algorithm in improving logistics efficiency, reducing operating cost, and saving transportation resources in the operations of two-echelon logistics networks.

Multi-period two-echelon location routing problem for disaster waste clean-up

Waste clean-up after a disaster is one of the most critical tasks in the response stage of disaster management. We develop a model to minimise the cost and duration of disaster waste clean-up considering using Temporary Disaster Waste Management Sites (TDWMSs), which can store and process waste before it is sent to the final disposal sites. The problem that arises can be seen as a Multi-Period Two-echelon Location Routing Problem (MP-2ELRP) in which the main decisions are the location of the TDWMSs and the routing of vehicles in both echelons. In this paper, we propose both a mixed-integer program and a Genetic Algorithm (GA) to model and solve the problem. Computational tests indicate: (i) the performance of proposed GA is robust; (ii) the use of TDWMSs can reduce both total waste clean-up cost and duration; and (iii) the capacities of TDWMSs have a significant impact on the total waste clean-up time and duration.

Design of the Distribution Network for a “Collect-on- Delivery” Company in a Metropolitan Context using Simulated Annealing with Path Relinking

Parcel delivery service by collect-on-delivery (COD, a.k.a. cash-on-delivery) companies is a new distribution mode in China. The design of the distribution network of a COD company in urban areas is of great importance and a relatively new research direction. In this paper, we aim to model this distribution n etwork as a two-echelon location routing problem (2E-LRP) and propose a novel efficient optimization algorithm by combining simula ted annealing (SA) and path relinking (PR) to solve this NP combinatorial optimization problem. The experimental results are reported for 84 test problems from Nguyen's, Prodhon's, and Sterle 's benchmark. They indicate that the proposed SA-PR algorithm is competitive with other existing state-of-art algorithms for 2E-LRP from the perspectives of both quality of solution and computational time. Therefore, SA-PR is an effective metaheuristic to solve 2E-LRP problems, i.e., design distribution network of a COD company in a metropolitan context.

A two-echelon location-routing problem for biomass logistics systems

Biomass has attracted considerable attention from both researchers and practitioners as an important renewable energy source that can help achieve sustainable development. However, inefficient biomass logistics systems hinder the development of biomass utilisation. This study investigates a two-echelon biomass resource location-routing problem (2E-BRLRP). Considering a predetermined supply of biomass resources, a mixed integer programming model for the 2E- BRLRP is established to determine the best locations for biomass collection facilities and corresponding vehicle routes. To address the computational complexity, a hybrid heuristic algorithm that embeds variable neighbourhood search into the tabu search framework is developed. A set of comprehensive computational examples are used to test the effectiveness and efficiency of the proposed approach. • This study investigates a two-echelon biomass resource location-routing problem. • A novel mixed integer programming model is established for the proposed problem. • A hybrid heuristic algorithm is developed for problem solution. • Comprehensive computational examples are conducted to verify the proposed approach.

Green logistics location-routing problem with eco-packages

Optimization of the green logistics location-routing problem with eco-packages involves solving a two-echelon location-routing problem and the pickup and delivery problem with time windows. The first echelon consists of large eco-package transport, which is modeled by a time-discretized transport-concentrated network flow programming in the resource sharing state–space–time (SST) network. The second echelon focuses on small eco-package pickups and deliveries, established by the cost-minimized synchronization-oriented location routing model that minimizes the total generalized cost, which includes internal transportation cost, value of eco-packages, short-term benefits and environmental externalities. In addition, the Gaussian mixture clustering algorithm is utilized to assign customers to their respective service providers in the pickup and delivery process, and a Clarke–Wright saving method-based non-dominated sorting genetic algorithm II is designed to optimize pickup and delivery routes, and improve their cost-effectiveness and degree of synchronization. Different strategy testing results are used in the service phase as input data to calculate the cost of the transport phase, which is solved through a Lagrangian relaxation approach. The 3D SST network representation innovatively captures the eco-package route sequence and state transition constraints over the shortest path in the pickup and delivery at any given moment of the transport phase. A large-scale logistics network in Chengdu, China, is used to demonstrate the proposed model and algorithm, and undertake sensitivity analysis considering the life cycle of green eco-packages.

Design of sustainable urban electronic grocery distribution network

To meet the expectation of multi-modal distributions from customers for last-mile delivery, a sustainable two-echelon E-Grocery delivery system is studied, which is motivated by the adaption of autonomous delivery robot (ADRs), parcel lockers in E-Grocery distribution industry. We formulate the multi-modal last mile system as a two-echelon location-routing problem with mixed vehicles and mixed satellites11Intermediate depot. (2E-LRP-MVMS). A multi-objective optimization model is developed to capture the characteristics of cost components and environmental impact. The goal of the 2E-LRP-MVMS is to determine the location facilities, to optimize the number of parcels delivered to two echelons and routes at each level, also to reduce costs caused by carbon emissions. A hybrid immune algorithm is proposed, and two improved steps, vaccination and immunization are introduced in the algorithm. This research contributes to the last-mile delivery network design domain by modeling the environmental and economic cost of E-Grocery distribution adopting mixed fleets and mixed satellites.

Presenting a Multi-Start Hybrid Heuristic for Solving the Problem of Two-Echelon Location-Routing Problem with Simultaneous Pickup and Delivery (2E-LRPSPD)

This study proposes a three-index flow-based mixed integer formulation to solve a two-echelon location routing problem with simultaneous pickup and delivery. In this formulation, pickup and delivery demands can be addressed using the same vehicle in each echelon of the network to reduce costs and increase logistics efficiency. We solve such NP-hard problem by developing a multistart hybrid heuristic with path relinking (MHH-PR) which is composed of local search and a variable neighbourhood descent algorithm. In the algorithm, three constructive heuristics are applied to generate diversified initial solutions, and path relinking is introduced for intensification and postoptimisation. Results indicate that MHH-PR can reduce the gap between the near optimal and global optimal solutions by 1%-2%. The proposed algorithm significantly improves computational efficiency by reducing the computational time of more than 10 min for existing cases involving 20 nodes to less than 10 s.

A Sustainable Multimodal Transport System: The Two-Echelon Location-Routing Problem with Consolidation in the Euro–China Expressway

Sustainable development of transport systems is a common topic of concern and effort in multiple countries, in which reducing carbon emissions is one of the core goals. Multimodal transport is an effective way to achieve carbon emission reduction and to efficiently utilize transport resources. The intercontinental transport system, represented by the Euro–China Expressway, is a prominent exploration that has recently received attention, which promotes the sustainable development of transport between countries and carbon emission reduction. In the intercontinental multimodal transport system, the reasonable connection of roads and railways, especially the optimization of consolidation, is an important link which affects the system’s carbon emissions. This paper focuses on the consolidation of sustainable multimodal transport and summarizes the multimodal transport two-echelon location-routing problem with consolidation (MT-2E-LRP-C). We aim to solve multimodal consolidation optimization problem, especially locations of multimodal station, by routing of highway and railway. We propose a two-layer mixed integer linear problem (MILP) model, which highlights the consolidation of roads and railways, focuses on road and rail transport connections, and optimizes road routes and railway schemes. To validate the MT-2E-LRP-C model, we design a series of random instances for different quantities of nodes. In order to solve large-scale instances and realistic transport problems, we propose a hybrid differential evolution algorithm, which decomposes the problem into a railway layer and a highway layer for heuristic algorithm solving. Furthermore, the MILP model and algorithm are tested by small-scale random instances, and the hybrid differential evolution algorithm is solved for the large-scale random instances. Finally, we solve the realist instance from the Euro–China Expressway to develop instructive conclusions.

A two-echelon location-routing problem with synchronisation

Motivated by an actual problem of a national postal service company, we introduce and define a new two-echelon location-routing problem (2E-LRP). The 2E-LRP is defined in a two-echelon distribution system where products are transported from origins to destinations through intermediate facilities. A major question that arises in a two-echelon distribution system is how to synchronise the flows of the two echelons at intermediate facilities. The synchronisation is important due to limited storage space or waiting times for transshipments at the intermediate facilities. In our new 2E-LRP, the activities in the two echelons are organised into two waves; a delivery wave, where products are sent from the primary facility to the customers through the intermediate facilities, and a following pickup wave, where the flow of products is reversed. The model only considers temporal constraints, assuming that capacities are never binding; the vehicles are always large enough given the constraints on time. As a solution approach, we propose a decomposition-based heuristic. Besides the solution approach, we propose data-driven schemes for use in combination with the model and we provide the computational results for different sets of instances.